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ANALYSIS OF SPALLATION TIME-OF-FLIGHT (TOF) NEUTRON DATA FROM A 2-D
POSITION-SENSITIVE DETECTOR
A. Schultz, P. Leung
To cite this version:
A. Schultz, P. Leung. ANALYSIS OF SPALLATION TIME-OF-FLIGHT (TOF) NEUTRON DATA
FROM A 2-D POSITION-SENSITIVE DETECTOR. Journal de Physique Colloques, 1986, 47 (C5),
pp.C5-137-C5-142. �10.1051/jphyscol:1986518�. �jpa-00225835�
ANALYSIS OF SPALLATION TIME-OF-FLIGHT (TOF) NEUTRON DATA FROM A 2-D POSITION-SENSITIVE DETECTOR
A.J.
SCHULTZ
andP.C.W. LEUNG
Chemistry and Materials Science and Technology Divisions, Argonne National Laboratory, ArgOnne, Illinois 60439, U.S.A.
A b s t r a c t
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The s i n g l e c r y s t a l d i f f r a c t o m e t e r a t t h e Argonne Intense Pulsed Neutron Source i s based on the t i m e - o f - f l i g h t (TOF) Laue technique and employs a 30 x 30 cm. p o s i t i o n - s e n s i t i v e s c i n t i l l a t i o n detector. The methods we use f o r producing r e c i p r o c a l space i n t e n s i t y p l o t s and f o r o b t a i n i n g i n t e g r a t e d s t r u c t u r e f a c t o r amp1 i t u d e s w i l l be described.I
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INTRODUCTIONAt t h e Intense Pulsed Neutron Source (IPNS), a t a r g e t o f depleted uranium i s bombarded by h i g h energy protons t o produce i n t e n s e b u r s t s o f neutrons by
spa1 l a t i o n . / l , 2 / Surrounding t h e t a r g e t are f o u r moderators, each w i t h several bean l i n e s which d i r e c t neutrons t o t h e various instruments. At a d i s t a n c e
r
from t h e moderator, t h e wavelength X o f a neutron i s determined by t h e de B r o g l i e equation:where h i s P l a n k ' s constant, m i s t h e neutron mass, and t i s t h e TOF f o r f l i g h t path
a.
The s i n g l e c r y s t a l d i f f r a c t o m e ~ (SCD) i s based on t h e TOF Laue technique./3/ I n t h i s paper, we w i l l describe some o f t h e procedures we'use t o analyze data obtained w i t h the SCD.I 1
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DATA COLLECTIONThe SCD employs a p o s i t i o n - s e n s i t i v e 6Li-glass s c i n t i l l a t i o n detector/$/ which 7s t y p i c a l l y centered on t h e 90' s c a t t e r i n g angle d i r e c t i o n a t a distance o f 32 cm.
from t h e c r y s t a l (Fig. 1). The s c i n t i l l a t i o n glass i s 30 x 30 cm., b u t due t o edge e f f e c t s , t h e a c t i v e area i s reduced t o about 27 cm. i n each dimension f o r a c t u a l data col 1 ection. Each neutron i s c h a r a c t e r i z e d by t h r e e d i g i t i z e d coordinates representing position on t h e d e t e c t o r (X and Y) and TOF (T). For each s t a t i o n a r y c r y s t a l o r i e n t a t i o n , data are accumulated f o r 2-12 hours (depending on sample size, u n i t c e l l size, etc.) i n a histogram w i t h t y p i c a l channel dimensions o f 85 x 85 x 120 corresponding t o X, Y and T r e s p e c t i v e l y . A f u l l hemisphere o f data r e q u i r e s up t o 35 c r y s t a l s e t t i n g s , i.e., 35 histograms.
Conceptually, t h e histogram i s constructed o f a stack o f 120 two-dimensional
"time-slices." The t i m e - s l i c e s are u s u a l l y set up w i t h v a r i a b l e widths ( ~ t ) such t h a t ~ t / t = 0.015. With a sample-to-moderator distance o f 660 cm., a sample-to- d e t e c t o r distance o f 32 cm., and a nominal wavelength range o f 0.7 t o 4.2 A,
neutrons w i t h TOF's between 1.2 and 7.3 mi l l i s e c . a f t e r to ( t h e s t a r t o f t h e pulse) are histogrammed, and ~t v a r i e s from 18 t o 110 psec.
Associated w i t h each t i m e - s l i c e i s t h e f r a c t i o n a l dead-time l o s s f o r t h a t p a r t i c u l a r t i m e - s l i c e . These values are obtained d u r i n g data c o l l e c t i o n by e m p i r i c a l l y determining t h e percentage o f t e s t s i g n a l s which are r e j e c t e d because
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986518
JOURNAL D E PHYSIQUE
DETECTOR ACTIVE ARE
PULSED SOURCE
Fig. 1
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A schematic r e p r e s e n t a t i o n o f t h e s i n g l e c r y s t a l d i f f r a c t o m e t e r a t t h e IPNS. Typical distances f o r a and a are 660 and 32 cm., r e s p e c t i v e l y . A low e f f i c i e n c y beam m o n i t o r (not shown) i$ l o c a t e d about 30 cm. from t h e c r y s t a l towards t h e source.the d e t e c t o r and t h e d i g i t i z i n g e l e c t r o n i c s are busy. A recent upgrade o f t h e d e t e c t o r has reduced t h e dead-time from 12 ~ s e c . down t o 3, such t h a t t h e maximum dead-time losses are u s u a l l y n o t more than 5%.
Each histogram i s archived on h i g h d e n s i t y magnetic tape, which can h o l d up t o 50 histograms per r e e l . The data a r e analyzed o f f l i n e on a VAX11/780 computer, as described below.
I 1 1
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PEAK SEARCH AND AUTO-INDEXINGOur peak search program, PEKSER, i s based on subroutine FRPEAK from t h e program FOURIER, w r i t t e n by R. J. Dellaca and W. T. Robinson a t t h e U n i v e r s i t y o f Canterbury (New Zealand), which i s d e r i v e d from A; Z a l k i n ' s FORDAP. The program outputs t h e l o c a t i o n s o f up t o 50 o f t h e most intense peaks i n a histogram. T y p i c a l l y , 5 t o 10 low order r e f l e c t i o n s can then be i n p u t i n t o t h e auto-indexing program BLIND,/5/
which was m o d i f i e d t o accept Laue data. By i n c l u d i n g a l l t h e s t r o n g r e f l e c t i o n s from a l l t h e histograms i n t h e least-squares program LSQRS, t h e accuracy o f t h e u n i t c e l l parameter and t h e o r i e n t a t i o n m a t r i x i s improved.
I V
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RECIPROCAL SPACE PLOTSA h i g h l y u s e f u l f e a t u r e o f t h e TOF Laue data obtained w i t h an area d e t e c t o r i s t h a t t h e histograms c o n t a i n i n t e n s i t y i n f o r m a t i o n f o r a s o l i d volume o f r e c i p r o c a l space i n c l u d i n g t h e regions between t h e fundamental Bragg r e f l e c t i o n s . This allows t h e user t o examine t h e histogram o f f l i n e f o r e x t r a Bragg o r d i f f u s e s c a t t e r i n g , which i s e s p e c i a l l y u s e f u l f o r searching f o r s t r u c t u r a l phase t r a n s i t i o n s a t low temperatures.16-81
The program RLPLN asks t h e user t o d e f i n e a plane i n r e c i p r o c a l space i n terms o f M i l l e r indices, which may be simply s e t t i n g h, k o r a t o a constant, o r p o s s i b l y r e q u i r i n g h = k f o r an hha p l o t . The user a l s o defines t h e range and t h e increments along each axis. I n t h e example i n F i g u r e 2, h = 4.93, k = -4.5 t o -1.5 i n steps
i n t e r p o l a t i n g i n three-dimensions using t h e formula:
where C i s t h e neutron count a t XYT normalized f o r i t s t i m e - s l i c e width, D i s t h e d i s t a n c e i n histogram coordinates between xyz and XYT, and t h e summations are over t h e nearest i n t e g e r l o c a t i o n t o xyz, (XYT),, and t h e surrounding 26 nearest neighbor l o c a t i o n s . Locations t h a t f a l l o u t s i d e t h e histogram l i m i t s are given i n t e n s i t y values o f zero. The a r r a y i s p l o t t e d as a 30 i n t e n s i t y p l o t w i t h a 100 x 100 g r i d u s i n g DISSPLA graphics r o u t i n e s (Fig. 2).
This program s t r a t e g y provides qua1 i t a t i v e o r s e m i - q u a n t i t a t i v e p l o t s which i n most cases are s u f f i c i e n t . / 6 - 8 / I f a more q u a n t i t a t i v e i n t e n s i t y p l o t i s required, c o r r e c t i o n s f o r t h e i n c i d e n t spectrum, t h e d e t e c t o r e f f i c i e n c y , dead-time losses and t h e Lorentz f a c t o r can be applied.
V
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PEAK INTEGRATION AND REDUCTIONFor a complete s t r u c t u r e analysis, i n t e g r a t e d Bragg i n t e n s i t i e s are obtained by c a l c u l a t i n g (using t h e o r i e n t a t i o n m a t r i x ) t h e l o c a t i o n s o f a1 1 p o s s i b l e r e f l e c t i o n s i n each histogram and i n t e g r a t i n g around t h e predicted histogram coordinates.
Because t h e wavelength r e s o l u t i o n from t h e source, AA/A, i s n e a r l y constant i n t h e thermal range, and since t h e t i m e - s l i c e widths vary such t h a t ~ t / t i s constant, t h e dimensions i n histogram coordinates o f a l l peaks are a l s o f a i r l y constant. The i n t e g r a t i o n l i m i t s i n terms o f histogram coordinates are d e f i n e d by t h e user a f t e r examination o f several r e f l e c t i o n s . Background p o i n t s a r e t h e histogram l o c a t i o n s surrounding t h e peak i n t e g r a t i o n r e c t a n g l e on each t i m e - s l i c e .
For each r e f l e c t i o n hka, the program checks t h e c d l c u l a t e d p o s i t i o n s o f i t s s i x nearest neighbors k1, k+l, a f l and t e s t s f o r p o s s i b l e overlap o f t h e i n t e g r a t i o n envelopes. I f t h e peak regions o f two r e f l e c t i o n s overlap, both r e f l e c t i o n s a r e rejected. I f t h e peak region o f one r e f l e c t i o n overlaps t h e background r e g i o n o f a second r e f l e c t i o n , then only those background p o i n t s which a r e a f f e c t e d are n o t i n c l u d e d i n t h e i n t e g r a t i o n . Each count used i n t h e i n t e g r a t i o n i s normalized f o r I t s t i m e - s l i c e width.
The conversion o f i n t e g r a t e d i n t e n s i t i e s t o s t r u c t u r e f a c t o r amplitudes i s based on t h e Laue formula:
where k i s a scale f a c t o r , T i s t h e normalized monitor count and FhkQ i s t h e s t r u c t u r e f a c t o r . The wavelength-dependent f a c t o r s are t h e dead-time l o s s c o r r e c t i o n T(x), t h e i n c i d e n t f l u x +(A), t h e d e t e c t o r e f f i c i e n c y e(A,r), t h e
absorption c o r r e c t i o n A(x), and t h e e x t i n c t i o n c o r r e c t i o n y ( x ) . Most o f t h e f a c t o r s i n equation (3) a r e f a i r l y s t r a i g h t f o r w a r d t o measure o r c a l c u l a t e , o r have been described p r e v i o u s l y 131. However, $ ( A ) and E ( x , ~ ) r e q u i r e some a d d i t i o n a l discussion.
Because t h e d e t e c t o r i s f l a t , n o t curved, t h e pathlength through t h e 6 L i - g l a s s o f .a neutron s c a t t e r e d from t h e c r y s t a l v a r i e s w i t h p o s i t i o n r on t h e detector, and
E i s not o n l y a f u n c t i o n o f wavelength A, but a l s o o f r. F i g u r e 3 shows t h e c a l c u l a t e d d e t e c t o r e f f i c i e n c i e s f o r a quadrant o f t h e d e t e c t o r based on t h e formula :
JOURNAL
DE
PHYSIQUEFig. 2
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P l o t o f t h e i n t e n s i t y d i s t r i b u t i o n i n t h e h =-4,93 r e c i e r o c a l l a t t i c e plane o f ~ - ( E T ) 2 1 3 a t 20 K./7/ S a t e l l i t e peaks a t (5,2,3)-q, (5,2,1)-q and (5,?,0)- q a r e c l e a r l y observable, where q = (0.07,0.27,0.21). The (hka)+q s a t e l l i t e s are observed i n a p l o t o f t h e h = 5.07 plane (not shown).where a(X) i s t h e l i n e a r absorption c o e f f i c i e n t i n t h e 6Li-loaded glass a t
wavelength
x
and e ( r ) i s t h e s l a n t path through t h e d e t e c t o r f o r neutrons s c a t t e r e d from t h e sample and e n t e r i n g t h e d e t e c t o r a t p o s i t i o n r. At longer wavelengths, a l l e f f i c i e n c i e s w i l l approach 100% such t h a t t h e dependence on p o s i t i o n w i l l ben e g l i g i b l e , but a t t h e s h o r t e r wavelengths o f t h e thermal spectrum t h e d i f f e r e n c e s are s i g n i f i c a n t . An analogous map t o t h e one i n F i g u r e 3 i s c a l c u l a t e d f o r each t i m e - s l i c e o f a histogram and t h e Bragg data are i n d i v i d u a l l y c o r r e c t e d f o r E ( x , ~ ) based on t h e wavelength and d e t e c t o r p o s i t i o n a t which they were observed.
The i n c i d e n t spectrum t e r m $ ( a ) i s based on incoherent s c a t t e r i n g data from a 3 mm. sphere o f vanadium a l l o y e d w i t h 7 a t . % niobium t o g i v e zero coherent
s c a t t e r i n g . The vanadium data are a l s o c o r r e c t e d f o r E ( x , ~ ) , i n a d d i t i o n t o c o r r e c t i o n s f o r t h e vanadium sphere absorption and dead-time losses. The f i n a l values f o r t h e i n c i d e n t source spectrum are obtained a f t e r s u b t r a c t i n g a background spectrum (no sample i n t h e sample p o s i t i o n ) from the vanadium spectrum.
We have r e c e n t l y c o l l e c t e d data a t 20 K on a 2 mm3 c r y s t a l o f B-(ET) I Br (ET i s
bis(ethylenedithio)tetrathiafulvalene,
o r BEDT-TTF) which has one f o r m f i l i weight o f C S H I Br per u n i t c e l l . The c r y s t a l s a r e t r i c l i n i c , P1, w i t h a u n i t c e l l voluii8hf
$ f o 2 i i 3 and w i t h 28 independent atoms. Data i n each o f t h e 35 histograms was accumulated f o r about 10 hours. O f t h e 5849 i n t e g r a t e d r e f l e c t i o n s , t h e 3285 w i t h F2> 5u(F2) were used t o r e f i n e 285 v a r i a b l e s which y i e l d e d R ( F ) = 0.053 and Rw(F2) 0.098. The standard d e v i a t i o n s a r e f0.002 A f o r C-C bonds and f0.004 A f o r C-H bonds.14 95.2 95.2 95.2 95.2 95.3 95.3 95.4 95.5 95.5 95.6 95.7 9 5 . 8 9 5 . 9 96.0 96.2 96.3 13 95.0 95.0 95.0 95.1 95.1 95.2 95.2 95.3 95.4 95.5 95.6 95.7 95.8 95.9 96.0 96.2 12 94.9 94.9 94.9 94.9 95.0 95.0 95.1 95.2 95.2 95.3 95.4 95.6 95.7 95.8 95.9 96.1 11 94.7 94.7 ,94.7 94.8 94.8 94.9 94.9 95.0 95.1 95.2 95.3 95.4 95.6 95.7 95.8 96.0 10 94.6 94.6 94.6 94.6 94.7 94.7 94.8 94.9 95.0 95.1 95.2 95.3 95.4 95.6 95.7 95.9 9 94.4 94.4 94.5 94.5 94.5 94.6 94.7 94.8 94.9 95.0 95.1 95.2 95.3 95.5 95.6 95.8 8 91.3 94.3 94.3 94.4 94.4 94.5 94.6 94.7 94.8 94.9 95.0 95.1 95.2 95.4 95.5 95.7 7 94.2 94.2 94.2 94.3 94.3 94.4 94.5 94.6 94.7 94.8 94.9 95.0 95.2 95.3 95.5 95.6 6 94.1 94.1 94.1 94.2 94.2 94.3 94.4 94.5 94.6 96.7 94.8 94.9 95.1 95.2 95.4 95.5 5 94.0 94.0 94.0 94.1 94.1 94.2 94.3 94.4 94.5 94.6 94.7 94.9 95.0 95.2 95.3 95.5 4 93.9 93.9 94.0 94.0 94.1 94.1 94.2 94.3 94.4 94.5 94.7 94.8 95.0 95.1 95.3 95.4 3 93.9 93.9 93.9 94.0 94.0 94.1 94.2 9C.3 94.4 94.5 94.6 94.8 94.9 95.1 95.2 95.4 2 93.8 93.8 93.9 93.9 94.0 94.0 94.1 94.2 94.3 94.5 94.6 94.7 94.9 95.0 95.2 95.4 1 93.8 93.8 93.8 93.9 93.9 94.0 94.1 94.2 94.3 94.4 94.6 94.7 94.9 95.0 95.2 95.4 0 93.8 93.8 93.8 93.9 93.9 94.0 94.1 94.2 94.3 94.4 94.6 94.7 94.9 95.0 95.2 95.3
XCM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Fig. 3
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A reproduction o f one quadrant o f t h e d e t e c t o r e f f i c i e n c y map a t awavelength o f 0.78 A. The lower l e f t h a n d corner i s t h e center o f t h e d e t e c t o r which i s t h e c l o s e s t p o i n t t o t h e c r y s t a l (32 cm.). The 6Li-loaded glass i s 2 mm. t h i c k .
V I
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CONCLUSIONSAs described above, s a t i s f a c t o r y r e s u l t s can be obtained w i t h t h e SCO, although they i n d i c a t e t h a t higher f l u x and b e t t e r r e s o l u t i o n a r e d e s i r a b l e f o r f u l l
s t r u c t u r a l analyses. I n a d d i t i o n , a technique f o r a c c u r a t e l y a b s t r a c t i n g t h e i n t e n s i t i e s o f weak r e f l e c t i o n s from t h e data would be useful. At t h e IPNS, a f a c t o r o f 3 i n f l u x may be achieved i n 1986 w i t h a new enriched uranium t a r g e t . At Los Alamos LANSCE and t h e Rutherford SNS s p a l l a t i o n sources, f l u x e s orders o f magnitude g r e a t e r than t h a t a t IPNS may be r e a l i z e d w i t h i n t h e coming years. Thus, t h e p o t e n t i a l o f t h e technique described i n t h i s paper may s t i l l l i e mostly i n t h e future.
For surveying r e c i p r o c a l space and studying s t r u c t u r a l phase t r a n s i t i o n s , we b e l i e v e t h e SCD has already proven t o be h i g h l y successful. We a r e i n t h e process o f p r o v i d i n g a d d i t i o n a l anci 1 la r y equipment f o r h i g h pressure, and lower and higher temperature studies. We a l s o plan t o increase t h e source-to-sample f l i g h t path t o p r o v i d e b e t t e r r e s o l u t i o n when t h e new t a r g e t i s i n s t a l l e d .
ACKNOWLEDGEMENTS
We wish t o g r a t e f u l l y acknowledge t h e c o n t r i b u t i o n s o f R. Brenner,
J. M. Carpenter, R. K. Crawford, R. A. Jacobson, S. W. Peterson, A. H. Reis, Jr., M. G. Strauss, R. G. T e l l e r , J. M. Williams and T. 6 . Worlton t o t n e development o f t h e instrument, software and data a n a l y s i s procedures associated w i t h t h e SCD. This work was supported by t h e O f f i c e o f Basic Energy Sciences, D i v i s i o n o f M a t e r i a l s Sciences, o f t h e U.S. Department o f Energy under c o n t r a c t W-31-109-Eng-38.
JOURNAL DE PHYSIQUE
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